Exercise 2 | Wiskunde op Tilburg University

Consider the demand function

$X(p)=\dfrac{1}{(p-2)^2}+3$ ,

$(p>2)$ . Determine the elasticity of the inverse demand function at

$X=4$ . Here, you may use that

$X(3)=4$ .

Antwoord 1 correct

Correct

Antwoord 2 optie

$-\frac{3}{2}$ .

Antwoord 2 correct

Fout

Antwoord 3 optie

$-2$

Antwoord 3 correct

Fout

Antwoord 4 optie

$-\frac{1}{2}$

Antwoord 4 correct

Fout

Antwoord 1 optie

$-\frac{2}{3}$

Antwoord 1 feedback

Correct:

$\epsilon^X=X'(p)\cdot \dfrac{p}{X(p)}$ .

$X'(p)=-\dfrac{2}{(p-2)^3}$ .

Hence,

$\epsilon^X=-\dfrac{2}{(p-2)^3}\cdot \dfrac{p}{\frac{1}{(p-2)^3}+3}$ .

At

$p=3$ :

$\epsilon^X=-\frac{3}{2}$ .

So, at

$X=4$ :

$\epsilon^p=\frac{1}{\epsilon^X}=\frac{1}{-\frac{3}{2}}=-\frac{2}{3}$ .

Go on.

Antwoord 2 feedback

Wrong: You have to find the elasticity of the inverse demand function.-2-2h

See Applications 2: Elasticity and inverse.

Antwoord 3 feedback

Wrong: Elasticity is not the same as a derivative.

See Elasticity.

Antwoord 4 feedback

Wrong: Elasticity is not the same as a derivative.

See Elasticity.